English spellings represent how words were pronounced hundreds of years ago. If you read old poems and pronounce each word like it's written, it will rhyme often rhyme where it wouldn't if you used the modern pronunciation. However, many words have different pronunciations now. This is particularly a problem with words ending in "gh". 'Gh" used to represent a consonant in English that was the same as German "ch" (this is very useful if you're looking for German-English cognates). This consonant no longer exists in most varieties of modern English (outside of Scotland), so "gh" is usually silent (sometimes it's pronounced as "f"). This has also affected the vowel before it in different ways. As you noticed, the "ei" sound is different in "height" and "weight".The disappearance of "gh" has also changed the way people pronounced "ei" in those words.

Because there is no one to one correspondence between how words are spelled and how they are pronounced in English. Just a simple fact of the English language that we all have to get used to at some point, native speakers included.